Least Common Multiple of 9 and 29

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 9 and 29 by Prime method
• Least Common Multiple of 9 and 29 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 29. First we will calculate the prime factors of 9 and 29.

Prime Factorization of 9

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 3²

Prime Factorization of 29

Prime factors of 29 are 29. Prime factorization of 29 in exponential form is:

29 = 29¹

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 29.

LCM(9,29) = 3²×29¹
LCM(9,29) = 261

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3, 9

Factors of 29

List of positive integer factors of 29 that divides 29 without a remainder.

1, 29

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 29, than apply into the LCM equation.

GCF(9,29) = 1
LCM(9,29) = ( 9 × 29) / 1
LCM(9,29) = 261 / 1
LCM(9,29) = 261

(i) The LCM of 29 and 9 is associative

LCM of 9 and 29 = LCM of 29 and 9

1. What is the LCM of 9 and 29?

Answer: LCM of 9 and 29 is 261.

2. What are the Factors of 9?

Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.

3. What are the Factors of 29?

Answer: Factors of 29 are 1, 29. There are 2 integers that are factors of 29. The greatest factor of 29 is 29.

4. How to Find the LCM of 9 and 29?

Answer:

Least Common Multiple of 9 and 29 = 261

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 29

29 = 29

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 261 = 3 x 3 x 29

Step 4: Therefore, the least common multiple of 9 and 29 is 261.